Is there any version of Action Script 3.0 for server side use?
No, Flash is client side. With Flex, you can communicate with a server (BlazeDS, ColdFusion, LiveCycle, or really anything).
You could theoretically run a standalone Flash (running in a browser on the server...) or AIR application to do stuff server side... but there would be better ways to do that.
Since ActionScript 3 is ECMAScript, there are couple of resources perhaps worth looking at that suggest server-side javascript is gaining some momentum and you may be able to get close to what you need
http://server-side-javascript.org
and
The Flash Media Server can run actionscript. Though only ActionScript 1, as far as I know.
You can read more her:
http://help.adobe.com/en_US/FlashMediaServer/3.5_SS_ASD/WSC604F694-2799-4472-8C55-684EF6D5224A.html
I would not really recommend it though, ASP.NET should be better in almost any case. One thing that you can do though is open a streaming connection and call code both ways. To do that in ASP.NET you would have to use sockets, doable but not as easy/quick.
As far as I'm aware there is no version of ActionScript 3 available for server side scripting. However, you might want to take a look Haxe. This language is similar to ActionScript 3 and targets multiple platforms like, JavaScript, Flash Player, PHP and Neko. By targeting Neko you can create very powerful server side applications using Haxe.
Any server could run any code as long as there was some type of environment set up on the server to interpret and run it.
So the question should be re-phrased "Are their any server environments that interpret Actionscript 3.0?"
While I'm sure someone has made one at some point, the answer is really no, because even if it exists, it's not widespread, and not on many (if any) servers. I do not know of any servers that have an environment installed on them that will run AS3 code. And I don't see it happening soon either, since many other languages have that niche filled quite well.
As an alternative, look to Java. Many servers will run JSP (Java Server Pages) and Java is quite similar to AS3 :)
Checkout Tamarin and redtamarin for running actionscript 3 server side. http://code.google.com/p/redtamarin/
in far future cold fusion will be powered by actionscript, maybe. There was demos for Adobe back in 2008 about running as3 on coldfusion as server side language.
Here is a survey from adobe http://www.surveymonkey.com/s/55FTCKJ
They are planning to bring ActionScript 3 to the server.